OBRABOTKAMETALLOV MATERIAL SCIENCE Vol. 25 No. 4 2023 Introduction Thermal expansion is an important thermal and physical property of materials, indicating the degree of materials’ extension upon heating. Knowledge of thermal expansion is of great interest not only from a scientific, but also from a practical point of view [1]. In assessing the potential uses of a material, thermal expansion becomes increasingly important in the production of parts and structures. Materials with low thermal expansion are widely used in electronic devices, thermal barrier coatings, precision equipment materials, thermal engine components, etc. [2]. In certain systems or composite materials, it is necessary to eliminate or even avoid thermal expansion mismatches between different materials, which can lead to the accumulation of thermal stress on the contact surfaces [3]. Thermal mismatch between the coating and substrate or between layers of a multilayer coating predominates during coating surfacing or heat treatment. Therefore, the resulting thermal stresses require a detailed analysis of the coefficient of thermal expansion (CTE) [4]. Oxide formation, residual stresses, and interfaces are characteristics of coatings caused by the thermal spraying process. Since volumetric expansion behavior is usually observed in thermally sprayed coatings, determining the correct CTE values is critical for designing and predicting coating characteristics under thermal loads [5]. Spray process parameters influence thermal expansion due to phase changes caused by oxidation, formation of compounds, etc. Thermal stresses arise from differences in CTE between the coating and substrate, and also arise as a result of the occurrence of a temperature gradient during the prolonged spraying process [6, 7]. It is also known that deformations due to thermal mismatch greatly affect the strength of component-coating bonding and the service life of thermal fatigue [8]. The coefficient of thermal expansion (CTE) quantitatively determines the expansion and contraction of a material due to temperature changes. The CTE of both the substrate and the coating strongly influences the adhesion strength of the coating. Significant changes in CTE can lead to deformation mismatch, causing cracks and degradation of the coating as a whole [9, 10]. The differences in thermal expansion coefficients at the interface result in a change in the local volume at the interface [11]. For example, in a coating on a Nibased superalloy, the deformation mismatch between the coating and the substrate creates internal stresses in the coating, leading to damage to the coating interface layers [6]. In-situ X-ray diffraction analysis is a reliable tool for assessing temperature-dependent properties of substrates and coatings. It helps to understand thermal expansion, crystallite size, grain growth, and changes in stress and strain with temperature variations [12, 13]. Based on the literature cited, it can be stated that volumetric expansion and lattice distortion can induce internal stresses in the parent material. Therefore, to detect material mismatch processes in terms of thermophysical parameters, the use of in-situ synchrotron X-ray diffraction is appropriate [14]. The full-width at half-maximum (FWHM) of X-ray reflections can reflect the evolution of internal stress under thermal loading [15, 16]. For example, changes in interplanar spacing due to thermal expansion are associated with a specific crystallographic orientation, while peak broadening occurs when lattice defects are present in a sufficiently large amount within the scattering volume, as well as in the presence of micro-stresses. As a result of thermal deformation mismatch, local residual stresses are generated, varying from grain to grain. The presence of grain-dependent lattice deformation along a crystallographic direction implies the existence of a distribution of interplanar distances (with a certain width Δdhkl) around a given “average” interplanar distance (dhkl) [17]. Sometimes, it is assumed that the intergranular stress state is constant and can, therefore, it can be ignored in the analysis. However, this assumption is often not valid [18]. The deformation of each grain depends on its orientation as well as the orientation of neighboring grains. If a grain is relatively “stiff” in a particular direction, the thermal stress in that direction induces plastic deformation in the “softer” surrounding grain. As a result, the deformation varies from grain to grain by an average magnitude, and the rate of stress decreases. The aim of this study is to interpret and utilize in-situ high-temperature X-ray diffraction as an effective tool for investigating the behavior of thermal mismatch between the substrate of VK8 alloy (92 % WC-8 % Co) and coatings of CrN, ZrN, and multilayer coating of CrZrN, as well as the characteristic
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